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UNIVERSALIZING TROPES - A SIMPLE WAY
Summary:
Donald Williams suggested that universals can be understood as sums or sets
of tropes under the assumption of a trope ontology. My goal in this article is
to present a less problematic and more convincing approach to the issue. It
consists of returning to the root of the problem, namely, the predicative
problem of how we can say the same of many. This is undoubtedly the real
problem, and my view is that trope theory does not require the resources of
universals as sums or sets of tropes to address it. One example of how this
kind of problem can be addressed without that resource was Berkeley’s solution
to the problem of general ideas using particular ideas in a generally
applicable manner. What I propose, in a nutshell, could be seen as the replacement
the Berkeleyan imagistic ideas with tropes. All that is needed is to develop a universalizing
ability, namely, the ability to follow a rule that enables us to identify
precise similarities between tropes used as models and those directly or
indirectly given to experience.
Key Words: trope theory, universals, ontology, Donald Williams.
My
goal with this article is to propose a new solution to the problem of
universals through the lens of trope theory. I claim that my solution is easier
and more effective than Donald Williams’s troublesome solution, thereby
considerably advancing the trope theory. In the first section, I explain the basic
ideas of trope ontology, as initially introduced by Williams. In section two, I
present his solution to the problem of universals employing tropes, showing its
shortcomings. In Section Three, I present the original Socratic-Platonic
problem that leads to the problem of universals, showing how it can divert us
from the real issue. Section four presents my solution to the original problem,
inspired by the nominalism of philosophers such as Ockham, Berkeley, and Hume.
This solution bypasses the old hipostasizing problem of universals insofar as
it shows it as a pseudoproblem. Section five sketches the application of the
solution to complex tropes.
1. Introducing trope
theory
In
his classic article “The Alphabet of Being” (1953 I-II), Donald Williams
introduced the theory of tropes through a suggestion as brilliant as it is simple.
His fundamental metaphysical thesis was that:
Any
possible world, and hence, of course, this one, is entirely constituted by its
tropes, and their connections of location and similarity and any others that
may be. (1953 I: 8)
This means that for Williams, tropes are the
universe-building pebbles. But what are tropes? He defined them as abstract
particulars because they can be abstracted from concrete particulars. His
example was of lollipops: we can separate the red of a lollipop, its shape, its
sweetness, its smoothness, its hardness, its weight... Although this definition
is technically correct, a more helpful way to say the same is to define tropes
as any spatiotemporally localizable properties. This contrasts sharply with
the standard use of the property concept in the philosophical tradition, where
it is understood as an abstract entity destituted of spatiotemporal localization.
Williams’ understanding of the extent of the trope
concept is made more evident by the following list that I take from his
article:
Color, shape, surface, odor, red, size,
triangularity... pain, love, sadness, pleasure, emotion, belief, serenity,
perception, discrimination, intention, disposition, power, mental processes,
sequences of thoughts... a smile, a sneeze... An election, a musical
performance, a love affair, a moral decision, an act of contrition, a piece of
impudence... the beauty of Mary, Mary being beautiful, the figure of a woman,
her complexion, her digestion...
This list shows us that tropes can be simple
properties (such as a red patch, a twinge of pain, or the whistle of a train)
or compound ones (a mental process, a sneeze, or a love affair). They can be
external (a smile, the figure of a woman), internal (sadness, serenity,
pleasures, dispositions, thoughts), or mixed (an act of contrition, a piece of
impudence). They can also be homogeneous (a violin solo) or heterogeneous (the
act of contrition, Mary’s digestion).
Considering
that tropes are spatiotemporally localizable properties, it is pretty clear
that even vague dependent empirical entities, such as the forces of nature, can
also be regarded as tropes, since they are localizable properties, though in a
more or less dispersed way. This can be said from the electromagnetism, the
gravitation, the strong and the weak forces. Because electromagnetic forces can
be separated from atoms in motion, gravity must be seen as the bending of the
space-time in the vicinity of massive bodies, strong forces can be drawn from
the interaction between quarks and gluons in the atomic nuclei, and weak forces
can be separated fromthe interaction between subatomic particles in atoms.
For Williams, tropes contrast only with concrete
particulars, such as, to use his examples, Mary, a church, and a nation. He
analyzed concrete particulars as sets of concurrent or compresent
tropes in the sense that their members are co-localized and co-temporal (1953:
8). They can be internally organized, like a particular human being or a
particular chair, or quite disorganized, as in the case of a particular rock...
Although concrete particulars are usually medium-sized dry objects, they can be,
as individuals, as small as electrons and atoms, and as large as stars and
galaxies.
As a standard
feature to all these concrete particulars, I would point to the rest mass. Rest
mass can be seen as a dispositional trope, absent in tropes like color, form,
weight, or a force of nature, but present in the set of compresent tropes that
make any concrete particular, so that under such and such circumstances, it
shows such and such a measurable reaction.
Finally, although Williams does not mention it, it
is worth noting here that we can apply here the Aristotelian criterion for the
difference between properties and substance: tropes can be predicatively
designated, while concrete particulars cannot.
William’s metaphysical project of building a world of tropes might be
demanding, but does not seem to be impossible.
2. Williams’ solution to the problem of
universals
In addition to trying to solve the question of
concrete particulars by resorting to tropes, Williams wanted to do the same
with the question of universals. Here is how he introduced it:
Speaking again approximately, the set or sum of
tropes precisely similar to a trope, say, that red, can, of course, be, or at
least formally correspond to, the abstract universal or ‘essence’ which can be
said to exemplify a definite sample of red. (1953 I: 9)
This convoluted definition can be presented
more clearly: a universal (essence) is a set or sum of tropes that are
precisely similar (Campbell 1981; sec. 6). The universal of the color red, for example,
is nothing more than the set or sum of tropes precisely similar (i.e.,
qualitatively identical) to a given trope of red. When I say that red is a
color, what I mean is that the set of all tropes of red (the universal essence
of red) is contained in the set of tropes of color (the universal essence of
color).
There
are problems with Williams’ solution. The most discussed has been that of the
infinite regress of tropes of precise similarity (for discussion, see Campbell
1990: 34-37). If the world is made up of its tropes, then it seems that the precise
similarity is also a trope. In this case, the precise similarities between the
tropes will need to be precisely similar, requiring a new class of precise
similarities. However, the tropes of this new class of precise similarities
will also need to be precisely similar, requiring a third class of precise
similarities, and so on, so that the result is an infinite regress.
There
are several ways to address this objection. Campbell, for example, suggested
that identity is an internal relationship between tropes that can only count as
a pseudo-addition with no real ontological basis (1990: 37). I prefer
not to harbor any prejudice against the thinness of any trope. I like to
think that since precise similarity is a relation dependent on the existence of
these tropes, it is itself a trope insofar as we tend to say it should be in
some way where those tropes are, but surely not as something found on
the other side of the universe or nowhere (that nothing exists nowhere is an
axiom of trope theory). And the same could be said of precise identity between
two precise identities. If these two are somehow localizable, then the precise
similarity trope between these precise similarities should also be somehow localizable.
The regress, in this case, exists, but it is not vicious because nothing forces
us to go forward. It remembers the harmless regress we find when we argue that
Plato required second-order ideas of ideas in the formulation of his doctrine
of ideas, and that he needed third-order ideas of those second-order ideas to
criticize his doctrine in the Parmenides. But this regression didn’t
need to go further since it was unnecessary. Similarly, we can stop by saying
that a class of precisely similar tropes demands the existence of tropes of
precise similarity between its tropes, but that this does not compel us to
appeal to a subsequent class of precise similarities between those precise
similarities, since this would be devoid of any explanatory function.
There
are other difficulties with Williams’s solution. Here are some of them. We do not
know whether the set of precisely similar tropes can be classified as a trope. Moreover,
sets have sizes and can increase or decrease, which seems to make them
different from universals. Moreover, universals do not appear to have any size,
especially if they are seen as essences, or as concepts, as common sense
suggests.
The biggest problem, however, which in my
judgment is fatal, is that sets of tropes that are precisely similar to each
other are usually too large to fit in our heads. That is, in most cases, indeed
in the vast majority of cases, the set of precisely similar tropes is cognitively
inaccessible to us. Consider, for example, the set of precisely similar
tropes of red: we can claim that it exists, of course, but not that any mind
has ever met it. And if it is an essence, then that essence turns to be
unknowable to us. It was suggested to me that they could be open sets. However,
open sets seem to exist in our minds, not in nature. Also, how many members
does this open set have? Can it be an empty set?
3. The problem of how we can say the same of
many
It
is essential to see that the so-called problem of universals arises from
another problem: “How can we say the same of many?” or “How can we apply the
same predicate to many different things? Here, we have the cognitive question
of knowing how it is possible to apply the same general term to a multiplicity
of things which are often very different. How is it possible, for example, to
apply the general term ‘justice’ to say that Socrates was just, that N. Winton’s,
noble action was just, or that the Finnish political system is just enough? The
question is not only linguistic. It is also epistemic since it concerns the
cognitive identification of unity in multiplicity.
The first philosophers to come across this
question were Socrates and Plato. Socrates wondered about the definition of concepts
expressed by general terms of philosophical interest, like justice, beauty, and
courage. Plato found a possible answer in his famous doctrine of ideas. As he wrote:
“I take it, we are in the habit of positing a single idea or form in the case
of the various multiplicities to which we give the same name” (Republic
596a 6-8).
As is well-known, the idea or form is unique
and abstract in that it is non-spatiotemporal, immutable (eternal), and capable
of definition; it belongs to an intelligible world that transcends the visible
world by being ontologically independent. And as is also well-known, he suggested
that by reference to the single idea or form, we can identify the various
things in the visible world that contain imperfect copies of them (by mimesis),
or that in some way share their being with that idea (by methéxis).
What is important to notice is that Plato
should be answering the question of how we can say the same of many,
which can be resumed as the question of predication, However, he moved from an
epistemological-linguistic problem to an ontological-metaphysical solution. As a result of this move,
the traditional problem of universals arose. Since the idea or form is
the universal, the problem of universals emerges as that of knowing “that
which by its nature is predicated of a number of things” (Aristotle 1984: 17a
38). This means the problem of the ontological nature of something objective
that, by itself, makes us capable of saying the same of many. For realist
philosophers such as Plato and Aristotle (under one plausible interpretation of
the latter), universals are abstract, immaterial entities, even if, in
Aristotle’s case, they are generally dependent on the existence of the things
constituting the visible world (Metaphysics:1034a 5-8).
Notwithstanding, there were not only realist
philosophers who moved from the epistemological-linguistic problem to an
ontological-metaphysical hypostazising solution. Some nominalist philosophers
have followed a similar path. This was the case of Peter Abelard, from whom the
general term has as reference the collection of things to which it
applies (Abelard 1994; 34; Wolterstorff 1970; 173). And this is also the case
of class nominalists for whom a general term must refer to its extension as the
class of objects to which it refers (Armstrong 1978: ch. 4; 1989: ch. 1). Thus,
a class nominalist might say that the class of all red objects must answer for
the applicability of a general term like ‘red.’ And D. K. Lewis (1986: 50 ff.),
a sophisticated class nominalist, would solve the problem of different general
terms with the same denotation but different connotations by appealing to their
application to the class of objects that encompasses all possible worlds since,
in that case, these classes would no longer need to coincide...
Now, the whole point of this digression is
that it seems pretty plausible that some form of collection or class nominalism
inspired Williams to propose his solution to the problem of universals as
classes of tropes precisely similar to each other. What he made was to replace
things, concrete particulars, with tropes as members of the class, which he treated
as a kind of “ersatz-universal.”
I call the solution to the problem of how we
can say the same of many by resorting to universals, beginning with
Plato, and ending with class nominalism, the “traditional solution.” And I tend
to believe this solution was a mistake that compromised more than two thousand
years of metaphysical research without substantial results, namely: the error
of offering an unnecessary ontological-metaphysical (hypostazising) solution to
a linguistic-epistemic problem. And I tend to think this move also infests
class nominalism as a bet on a class as a kind of “ersatz-universal”. As Plato
made this mistake in the beginning, it gave rise to a tradition of
investigating universals so ingrained that its linguistic-epistemic origin was often
forgotten, becomming a challenging work to dislodge it from the minds of
philosophers.
Not all philosophers, it is true, have
fallen into this trap. William of Ockham suggested that all we need is to
develop the mental capacity to recognize the right similarities in many
different things (1995: 43-45), and to speak of universals is to speak of this
capacity. And throught their particularism, Berkeley (1710: Intr.) and Hume (1740:
I, I, VII) were also honorable exceptions. According to Berkeley’s
immaterialism, as is well known, the whole world (except for the Spirits) is
constituted of particular ideas of purely mental (and not Platonic) nature.The things of the so-called external world
are nothing more than more intense and organized ideas that impose themselves
on us (Berkeley 1710: I, sec. 30). One idea can be general in the sense that it
applies to many different things. But for him, they are never abstract,
which means that they never have the function of Platonic universals or
anything other than their purely mental nature. As he wrote:
It
seems that a word becomes general by being made the sign, not of a general
abstract idea, but of several particular ideas, any one of them indifferently
suggested to the mind (Berkeley 1710: Intr. Sec. 11)
That
is: a general term is associated with mental ideas; for example, the general
term triangle is related to images of several particular triangles, equiangles,
rectangles, obtuse... On this basis, we are able, whenever we have access to a
given triangle in the external world (that is, to an “external” idea of a
triangle), to compare it with an idea of the ideas that we have associated with
the general term, applying this term to the given triangle in the so-called
external world. To explain this operation, Berkeley does not needed to resort
to reyfied universals at any time. He only compared the idea given in the
experience with ideas he has in mind that he associated with some general term.
Then, when he perceived their similarity, he applied the same general term to
the idea given in the experience. David Hume added to Berkeley’s proposal a
number of diferent but approximated ideas a same general term (1740: 17).
I can
anticipate that my strategy will be structurally analogous to those of Berkeley
and Hume, for what I wish to do here is essentially replace “idea” with “trope”.
However, I will be free from the main criticism of Berkeley's solution to the
problem of predication, which is that it is an imagistic solution and
that many concepts do not require the formation of images or only require them
secondarily.
Since tropes need not be essentially
imagistic, even if they must be somehow derived from sensory experience, my
approach will not be open to this accusation.
In what follows, I want to propose my
solution to the problem of how we can say the same of many, inspired by
Berkeley’s strategy. Although based on the theory of tropes, this solution does
not need to answer the epistemological problem through an ontological solution.
It will be an alternative move that dispenses the appeal to universals dealt
with in the traditional answer.
4.
Universalizing Skills
In
conformity with the suggested line of thought, I propose we learn to say the
same of many by gaining a skill. It is the ability to (i) associate a trope
with its corresponding general term; (ii)
use this same trope (or any others that are precisely similar to it) as a model
to compare with any trope that we are given to consideration, in order to be
able to tell whether or not it has a precise similarity with the tropes used as
a model. Once this skill is acquired, we can say the same of many without
resorting to universals or classes of tropes as universals. We can call this
skill a universalizing ability.
I want
to start with a straightforward example. Suppose Mary has taken a painting
course and learned to identify the color ‘land of Sienna’. To this end, she had
eye contact with many examples of this color, having learned to associate these
examples with the color’s name and remember precisely this model color trope.
Later, she takes a trip to Italy. There, she identified many buildings painted with
the colors Land of Siena. All she needed to do to name the color of these
buildings correctly is to have the memory of a particular trope and be able to
identify new tropes precisely similar to it. She developed the ability to
recognize the land of Siena trope. She learned to say the same of many
regarding this general term. Obviously (to her luck), she does not need to
resort to the immense set of land of Siena tropes that are precisely similar be
able to use this general term predicatively. Maria’s universalizing ability concerning
the land of Siena trope can be specified as the hability to identify any land
of Siena trope that is given to her experience as being precisely similar to the
model tropes she remembers to have seen as she learned the reference of the
general term ‘land of Sienna’. We also say that Mary has learned to use
the word ‘land of Siena,’ that she knows its meaning, that she mastered
the concept or conceptual rule for the word’s application.
Finally, the rule followed by Mary is also a trope, a complex trope that
involves her memory of the land of Sienna trope and her identification of new
tropes as precisely similar to the first one.
Two points are worth mentioning. The first
is that memory isn’t a problem. It is like a copy we learn to trust as it works
well enough to be considered trustworthy. Its trustworthiness is bestowed
through interpersonal comparison between what has been identified and what has
been reidentified. Moreover, it is importante to see that memory is an
intermediary that is not even a necessary part of the procedure. The second
point is that this ability is always, at least in principle, capable of
generating an extensional class of tropes—but a class that has no relevance
whatsoever in solving our problem of saying the same of many.
We can highlight these points by resorting
to a language game that shows the essence of the universalizing procedure. Imagine
that a group of people with a particular mnemonic deficiency are in an
exhibition of paintings, and are given a task: to identify the paintings in
which the color of Sienna appears. There are 12 numbered paintings. Each person
receives a tablet where the name ‘Land of Sienna’ is found next to a circle
painted in the same color and twelve squares corresponding to each of the 12
paintings. All they need to do is mark the spaces corresponding to the
paintings that feature the color of the land of Sienna. By taking the tables
with their painted circles close to each painting, they can mark the spaces
corresponding to the paintings in which a color precisely similar to the model
is found. By doing this, people carry out a universalizing practice without
resorting to long term memorized patterns. Finally, let’s say that the only
frames with these color tropes are 2, 3, 8, and 12, and that this shows up as a
result in the correctly marked tables. With this, they found, within a very
narrow domain, a set of land of Sienna tropes that are precisely similar: the
extensional set {2, 3, 8, 12}. It is clear that this set is of no use to us. It
has no explanatory force concerning our ability to say the same of many.
What the people in the example do is that
they follow a rule that tells them to compare the color model trope of
the tablet with the color tropes found in the paintings in search for precise
similarities. The model trope that they see, as much as the model trope we usually
actualize in our memory, serves as a criterion for applying the rule. The rule applies
when people mark the square on the tablet corresponding to the trope where the land
of Sienna trope is found. Since we say this person now has the concept of the
land of Sienna, there is nothing more natural than considering this universalizing
ability a conceptual rule or concept, which is nothing beyond the
trope of a repeatable spatio-temporal procedure.
Returning to our problem, we can now define
the universalizing ability (the “universal” in a harmless sense) as follows:
Universalizing
ability concerning a general term G by the epistemic agent S (Df.) = S’s
ability to, having associated G with a model trope Tm, be able to use
it as a criterial rule capable of allowing the identification of any given
trope T as being or not being precisely similar to Tm.
The
universalizing ability is the hability to follow a conceptual rule corresponding
to what we ordinarily call a concept. Like everything else, this rule
must require a replicable trope that will be found in every application of G, not
as something metaphysically abstract in any realist sense. The memorized model
trope Tm serves here as a
criterion to be satisfied by some given trope T.
5.
Universalization of complex tropes
So
far, we have exemplified our universalizing ability relative to a trope that
can be classified as perceptually simple: the color called ‘land of Sienna’.
But what about more complex cases, such as the other tropes named by Williams,
tropes such as those of triangularities, sneezing, smiles, sadness, a thought, and
an act of contrition?
I believe that anyone who has read the
constructive particularist procedures of John Locke would find the achievement
of the above described universalizing ability also applicable to complex tropes
(1979: Book II). Locke started with imagistic ideas and combined them to form
more and more complex and diversified ones. The difference is that here, we do
not start with ideas or qualities, as Locke did. We start with simple tropes
(that include his ideas and qualities), combining them to form more complex and
diverse tropes that may appear to recur to abstract universals in the independence
of empirical foundation, since they cannot be easily traced to their origins.
But we use their memory as a criterion for identifying precisely similar tropes
that are precisely similar to them, and in doing so we are applying the same
universalizing skill exemplified above.
In what follows, I will analyze a few
complex tropes to demonstrate that they can be viewed as spatiotemporally
localizable particulars without any abstract quality in the realistic
(Platonic-Aristotelian) sense. To do so, it is necessary to define or decompose
these tropes analytically as far as we can, showing that although they are not
as directly and immediately identifiable as in the case of the trope of the
land of Sienna, they are composed from tropes that can be found in sense-experience
or derived from it. The goal is to make it plausible that the universalizing
ability acquired in the cases of more complex tropes does not differ essentially
from the intuitive case of a simple trope like ‘land of Sienna’.
Let’s start with the straightforward case of
the complex external trope of sneezing. It can be assumed that our ability to
use general terms is acquired interpersonally, through both positive and
negative examples (Tugendhat 1976, lecture 11). Thus, we usually learn the
concept of sneezing by observing that adults give this name to the act of
sneezing, whether it is ours or someone else’s, so that we are praised when we
get it right, and we are corrected when we make a mistake. In this way, we
acquire the universalizing ability to identify sneezes, which are themselves dispositional
tropes. This is also about learning the concept (the tropical rule of
conceptual application) based on our memories of sneeze tropes. As this rule is
tacitly understood, we do not generally know how to verbalize it. But
dictionaries help us, defining sneezing as “an involuntary movement of the
airways to expel any foreign substance from the body.” This definition makes explicit
what we mean by naming the complex sneeze trope; it works as a criterion for
the application of the criterial conceptual rule, as much as the land of Sienna.
To have the concept of sneezing is to have a dispositional procedure
or rule understood as a dispositional trope that enables us to identify
tropes that satisfy the definition. Since this disposition is a trope, it
should not be confused with the tropes it is made to identify.
Let us now look at the relatively simple
trope of triangularity, also recalled by Williams. Here, learning is also tacitly
done through interpersonal examples. We are presented with equiangular
triangles, acute, obtuse, rectangles... until we learn not an abstract triangle
typical to all of them (as Berkeley famously accused Locke to have suggested),
but to vary the internal angles of a model triangle trope, so that we can form
the corresponding images of triangles given in the experience. By doing this,
we have already learned a tacit definition of a triangle, which can be
explicitly formulated as “A triangle = a three-sided polygon.” Such a
definition decomposes the internal tropes of the triangle into those of a three-sided
polygon. (We can compare our use of the definition with a machine in with which
by varying the input we can get a diferente output, namely, a diferent
triangle, which shows that we do not need any abstract idea of a triangle in
order to recognize triangles.)
Now, consider Williams’ internal trope of
sadness: all we need to universalize is to be able to identify instances of sorrow
that are precisely similar to tropes of sadness that we have already learned to
identify by different means in other people and ourselves. Moreover, we use
these memorized tropes as models for identifying further cases of sorrow.
Dictionaries characterize this trope as “a feeling of despondency, melancholy,
unhappiness, and hopelessness.”
Let us now examine the mixed and complex
trope of the act of contrition mentioned by Williams. As I was informed, it is a
Christian prayer that asks for repentance for sins and mercy from God. All we
need to universalize are examples of acts of contrition in memory, or, in my case,
explicit information about this trope, which allows us to imagine it and
identify precisely similar cases.
I now want to consider two examples that Williams
did not mention of countable tropes. They differ from the previous ones since
they are concerned with the essence of concrete particulars. A first
example is that of an artifact name: the trope of chair (from ‘to be a chair’).
This is a complex external trope. We all know what a chair is, but we have
difficulties defining it since we have learned the conceptual rule for the
identification of chairs in a tacit or implicit way. However, we can give the
following reasonable definition of a chair:
Chair
trope (Df.): a non-vehicular seat with a backrest made for one person to
sit at a time.
It
would not be a chair but a simple bench if it had no backrest. It cannot be
found in vehicles such as cars, planes, or trains because, in that case, they
will be called seats. They must be made so that only one person can sit on them
each time; otherwise, they would be sofas. Even if a chair were teletransported
to a planet where people were very slim, and several of them could sit in the
same chair, it would not turn into a sofa, since as an artifact it was made
for only one person to sit on at a time. A chair that has not been made as an
artifact, say, a chair carved into the rock, is only a metaphorical chair, no
less than a toy chair.
We cannot directly perceive a chair trope.
It is not written on a chair that it should be a bench with a backrest, that it
is made for one person to sit at a time, or that it may have been the work of a
carpenter. But we can build all this conjoining perceptible tropes in space and
time.
That is why it took a good number of
experiences of positive and negative examples so that we could gradually
tacitly learn the complex trope, linguistically expressed in the definition of a
chair. Afterward, keeping in mind the external, complex, and articulated trope
that we associate with the word chair, we can identify precisely similar tropes
of “chair”, such as those that exist when we encounter table chairs,
wheelchairs, beach chairs, electric chairs, thrones... Of course, the
dispositional conceptual rule used to identify chair tropes cannot be reduced
to something we can have a mental image of. Neither tropes nor the tropical procedures
of universalization force us to a purely imagistic conception of reality, once
the relations among images established by the conceptual rule expressed above
cannot be reduced to images alone.
Someone may now ask a challenging question: How
can I distinguish the trope of “chairness” from the concrete particular that is
a specific chair? After all, this trope is a combination of spatiotemporally
locatable tropes present, and where a chair is found, one will also find a
complex trope of this chair. The answer lies in the spatio-temporal location of
the object, which will always be distinctive. However, insofar as we can
identify a particular chair apart from its spatiotemporal location, the answer is
that a concrete particular is constituted by many other tropes besides those
that definitionally constitute it. These accidental tropes do not define it,
but help us identify the concrete particular. For example, the chair I’m
sitting on now has soft upholstery. It is made of plastic and wood, faded
yellow and old, and was bought in a second-hand furniture store. These are not
elements of the trope of the chair I sit in, but of this concrete particular.
Hence, the concrete particular must be a conjunction of present tropes that extrapolate
its definitional trope. This answer can also be applied to other countable
names of “essences” like the one in the following example.
Let us consider, finally, a much-talked-about
trope of the countable concept of natural species: that of the human being,
traditionally defined by the Greeks as a rational animal but characterized
today in dictionaries as “a bipedal primate endowed with reason, culture, and
advanced language.” Of course, this characterization of the complex trope
cannot be directly perceived in our immediate sensory experience of other human
beings. However, it was also learned tacitly through many positive and negative
examples, even if we are unable to articulate the explicit dictionary
definition. Indeed, I have already seen many of these bipedal primates and learned
to recognize myself in the mirror as one of them. I know they can have a
certain degree of reason, culture, and advanced language. It was through this
public learning arising from extraordinarily complex spatio-temporal articulations
of simple imagistic perceptual tropes that I gradually learned what human
beings are and that I became able to use my knowledge of the complex trope
associated with the general term ‘human being’ as a rule to recognize, at least
aspectually, precisely similar trope articulations in the cases of the most
diverse beings recognizable as humans. I do not need to form images of this
trope, since, as a whole, it is unimaginable. However, with the conceptual
rule, I can produce associated images and their combinations. We would say that
the conceptual rule expressed by the word ‘man’ is a trope allowing us to associate
the memory of an extraordinarily complex articulation of tropes with any
precisely similar articulation of tropes we can find in the external world.
4.
Conclusion
By
the given arguments added to the Analyse of some few examples, I hope to have
shown that constructing our predicative capacity as an hability of following a linguistic
rule enabling us to identify complex tropes in the empirical world through
their implicitly known definitions or characterizations abstracted as
model-tropes is in principle feasible and, from the viewpoint of trope theory,
a more promising endeavor than Williams resource of classes or sums of tropes
as reifying “ersatz-universals”.
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